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Cr53 (p p )Cr53 and Cr53 (p n )Mn53 Reactions.

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162
Annalen der Physik
*
Cc5'(p, p'y)Cc'' and Cc5'(p, n y)Mn''
7. Folge
*
Band 20, Heft 3/4
*
1967
Reactions
By M. A. ABUZEID,M. I. EL-ZAIKI,N. A. MANSOUR,A. I. POPOV~),
H. R. SAADand V. E. STORIZHKO~)
With 6 Figures
Abstract
Total yields and angular distributions of 380 keV gamma rays from the Cr53 ( p ,n y ) MnS3
reaction have been measured for proton energies below 2.5 MeV. The experimental results
are in good agreement with predictions of the statistical compound-nucleus theory. The
angular distributions of 560 keV gamma rays upon the proton inelastic scattering on C P
at E, =. 2.3, 2.4 and 2.5 MeV are isotropic, which is commensurate with a 'I2- assignment
t o the first excited state of C P .
1. Introduction
The status of the compound-nucleus (CN) correlation theory for inelastic
nucleon scattering has recently been reviewed both from the theoretical point
of view and from the relevant experimental data [I]. It has been found that
the theory is very successful in explaining numerous measurements of the
correlation function for neutron and proton inelastic scattering from mediumheavy nuclei. At present, the available data for ( p , n y ) and ( n , p y ) reactions are'
somewhat meagre, and the degree of validity of the CN correlation theory for
such processes is not known. Recently, the inelastic scattering of protons on
Cr5O and Cr54has been studied in this laboratory a t proton energies below 2.5MeV
[2]. The experimental results for angular distributions are in reasonably good
agreement with the predictions of CN theory. This motivated us t o investigate
the W3 ( p ,n y ) Mn'3 reaction.
Measurements on the C r t 3 ( p , n )MnE3reaction in the energy range E , =
1.42 - 2.47 MeV were reported by LOVINGTON
e t al. [3], who observed more
than one hundred resonances in the neutron yield. Gamma radiation from this
reaction has been studied by MCCLELLANDE
e t al. [4] and VALTERet al. [5)
with a single crystal NaI(T1) spectrometer. Using a thick natural Cr-target,
the total yield of 380 keV y-rays for an E, = 1.6 .. . 3.2 MeV and also the
angular distribution at E , = 2.6 MeV have been measured [5]. I n a more
recent investigation, KIM [61 studied fluctuations in the differential crosssection of the Cr53( p ,n ) Mn53reaction.
I n this paper we report the results of the cross-section measurements of
( p , p ' y ) and ( p , n y ) reactions on Cr53 in the proton-energy region E , = 1.8
.. 2.5 MeV.
1)
On leave from Physico-Technical Institute, Kharkov, USSR.
163
M. A. ABUZEIDand co-workers: Cr53(p,p'y)Cr53and C ~ - ~ ~ ( p , n y )Reactions
Mn~~
2. Experimental Arrangement
Protons were accelerated by the 2.5 MeV electrostatic generator of the UAR
Atomic Energy Establishment. After momentum analysis, the incident beam
was focussed onto a target by quadrupole lenses. The target chamber was a
cylindrical brass cup 3.0 cm in diameter with a wall thickness of 0.05 cm. Selfsupporting enriched chromium targets were used. Table 1 shows the isotopic
composition and thickness of the targets. After passing through the target
the beam was stopped in a 5011 gold foil in order t o reduce the background.
The total charge delivered t o the target was measured with a current integrator.
Table 1
T h i c k n e s s a n d enrichment of t h e Crb3 t a r g e t s
Percentage of isotopic impurity present
Target
Nucleus
(350
I
(352
I
Crs
I
Cr54
Target
thickness
mg cm-2
-
Single gamma-ray spectra were measured using 2"x 2" NaI(T1) crystals and
recorded with a transistorized RCL-512 channel pulse-height analyser. Fig. 1
displays a typical gamma-ray spectrum taken a t E , = 2.5MeV. It can be
seen t h a t 200, 380 and 560keV gamma-rays are present. The origin of the
200 keV line has not yet been established, but it may be due t o a neutron
irradiation of the NaI(T1) crystal. The 380 keV line corresponds t o the decay
of the M d 3 first excited level in the W 3 ( p , n )M d 3 reaction. The ground state
threshold energy of this reaction is equal t o 1380 keV [7]. The 560 keV line
resulting from the inelastic proton scattering corresponds t o the decay of the
first excited level of W3.
380
053, P
Ep=E50HeV
8=90"
I
70
I
20
I
60
50
CHANNEL NUMBER
30
I
J
60
0
Fig. 1. Pulse-height distribution of gamma-rays
from the enriched Crm target taken at F, = 2.5MeV
11*
I
30
-Bo
a
I
60
90
Fie. 2.
Gcmma-ray angular distributions
for the CP((p,p'y)Cra reaction.
Solid lines are least squares fits to
experimental distributions
164
Annalen der Physik
*
7. Folge
*
Band 20, Heft 3/4
*
19Gi
3. Results of the Measurements
The angular distributions of 560 keV gamma rays following the inelastic
scattering Cr53(p,p‘y)Cr53 have been measured a t E , = 2.3, 2.4 and 2.5 MeV.
Fig. 2 shows the results of these measurements. All these angular distributions
are isotropic, which is commensurate with a
assignment [8] t o the first
excited state of Cr53.The uncertainties are statistical errors only.
The angular distributions of 380 keV gamma rays from the Cr53(I),
reaction have been measured for the proton energy range 1.9...2.5MeV in
steps of 100 keV. Fig. 3 shows the results of these measurements. Statistical
errors in the recorded counts were negligible and are not indicated in Fig. 3.
All the angular distributions are similar t o those measured a t E , = 2.6 MeV
by VALTER
et al. [ 5 ] . The gamma ray yield, for proton energies 1.9 t o 2.5 MeV,
has been measured a t an angle of 56” with respect to the proton beam direction
Fig. 4 shows the total gamma ray yield from the Cr53(p,ny)Mn53 reaction
obtained from these measurement,s.
1
I .
I9
-
20 2.7 22 23 24 2 5
Ep (MeVl
Fig. 3.
Gamma-ray angular distributions for
the CrSS( p , n y )Mn53reaction. Solid lines
are the theoretical CN fit
Fig. 4. Total yield of the 380 keV gamma
rays from the Crm(p,ny)Mns reaction. The
solid line is the theoretical CK fit
4. Data Analysis
The angular CN correlation theory developed by HAUSER
and FESHBACH
[9],
SATCHLER
[lo], and SHELDON[I] for inelastic nucleon scattering may be
generalized for the (p,ny) and (n,py) processes. Energy levels involved in the
CrE3 + p reactions are shown in Fig. 5 . Following SHELDON
[l]we can write
t h e differential cross-section of the Cr53( p ,n y ) Mn53 reaction for a transition
M. A. ABUZEIDand co-workers: W3( p , p ' y ) CrS8 and Crj3 ( ~ , n y ) MReactions
n~~
165
J,,(j$*)) J1( j $ + ) )J2(LL') Js (intermediate radiation is not observed) in the form:
dU
- 2'
(-)JL*)-Jl-Jz
a-8
[Cj1
(32)2/(j~)21
)3
6 (&! T A(ji*) i$*)J OJ1)
x 1"2.(J3J2)
W(J1J,J2J,; Aja*)) T P A(cos O ) ,
with the summation over all permitted values of A, J1 and jb+). Here
R(J3J2) FE
(1
+i l y .
[F).(LLJ3J,)
+
2dF1(LL'J3J2)
(1)
+ 42F~(L'L'J3J,)I
fin"
Fig. 5. Energy level diagram showing
the transitions that were studied in
the present work
The mixing ratio A 2 =
'
"L'llJa)'- FAand 71 are functions tabulated by FERENZ
!J311L11J2)a
+
and ROZENZWEIG
[ll]and SATCHLER
[12]; j = (2J 1)1/*.The symbol d(*)
confines the summation t o terms where the pairs of j ( * ) va.lues are numerically
equal. The z terms are:
t
= fi?)(-WT i 3 3 2 )
i3
Tl*)(E),
(2)
where T(*)
are generalized transmission coefficients (1). The total cross section
for the CN mechanism may be written:
1
a = - - n2R 2
c
[(j1)/@o)l2 t.
(3)
Jl,jL*)
For the proton energy range studied, 1.9 t o 2.5 MeV, the average excitation
energy of the levels in the MnM compound nucleus is 9.7 MeV. The mean CN
level spacing was calculated using the GILBERT-CAMERON
[13] theory and was
found t o be 0.25keV. I n our measurements chromium targets were about
300 keV thick at the energies used. Therefore, many levels of the compound
nucleus were excited, and the statistical model could be applied. However, it
should be noted that, a t low bombarding energies, the effective CN level
density may differ considerebIy from the calculated one, and the statistical
assumption may be violated. Additional assumptions were introduced in the
analysis of the Cr53(p,ny)M d 3 reaction: 1) only protons with 1 = 2 and
neutrons with 1 = 3 contribute essentially t o the reaction; 2) the direct process
cross section is small compared t o the CN cross section; 3) the only competing
processes are the Cr53(p,no)Mn53reaction and proton inelastic scattering, the
cross section of which is small compared t o t h a t of the ( p , n) reaction. All these
assumptions are well satisfied in the proton energy range studied. A general
166
Annalen der Physik
*
7. Folge
*
Band 20, Heft 314
*
19G7
form of the differential cross section for the (p,ny) reaction on a non-zero
spin nucleus is quite cumbersome and not given here. The neutron transmission
coefficients T i * ) ( E )were obtained through interpolation from the tables pub[14]. The optical model potential was of the form:
lished by NEMIROVSKY
V
=
(1 + i t ) ,
V,exp[-a((r-R')]
v = VO(1 + i t ) ,
rrR',
r 2 R'.
(4)
cm2,
(5)
The parameters used in the calculations were :
V, = 50 MeV,
E = 0.06,
a
R,
1.55fm,
= 1.24. All3 fm.
x = 2.8.
=
These parameters were obtained from an analysis [14] of the total cross sections
and angular distributions in the energy region below 1 MeV. The proton transe t al.
mission coefficients have been calculated using the method of FESHBACH
1151.
I n Fig. 3 solid lines represent results of the theoretical calculations for the
angular distributions of gamma rays from the Cr53( p ,n y ) Mn53 reaction. The
experimental and theoretical curves have been normalized arbitrarily. The
value [8] of the mixing parameter d = 1.2 for the gamma transition 380 keV
c
g.S. i n Mn53has been used. As can be seen, the predictions of the CN theory
are in reasonable agreement with the experimental results. The calculations
without the inclusion of spin-orbit interaction display a n equally satisfactory
agreement; the only marked discrepancy occurs a t E , = 1.9 MeV. However,
the results of these measurements for this energy are, t o some extent, uncertain,
since a contribution from the Cr52(p,y)Mn53 reaction may be essential. The
measurements with an enriched Cr52 target show a larger anisotropy in the
angular distributions for this reaction.
Because of a small anisotropy in the angular distributions, the accuracy
involved in the determination of the mixing parameter is very low. For this
reason, the angular distributions for E , = 2.2, 2.3, 2.4 and 2.5MeV were
averaged. The averaged distribution anisotropy A = -0.072 f 0.014 was
determined by a least-squares fit from the ratio A = (I A2)/(1- 0.5.4,) - 1,
where A , is the coefficient in the expansion W ( 0 ) = 1 A,P,(cos 0). (The
shaded area in Fig. 6.) The averaged distribution anisotropy is compared with
+
+
0
0.5
I
A
2 345
0)
-A
0.70
008
a06
Or04
0.02
O0
30"
600
t0n-q
--c
900
Fig. 6. Experimental asymmetry parameter
(shaded area) and theoretical predictions for
different values of the mixing parameter A
(solid line)
M. A. ABUZEIDand co-workers: Cr5a(p,p’y)CrSSand Cr53(p,ny)Mn53
Reactions
167
theoretical predictions. The solid line represents the results of the CN fit for
various values of the mixing parameter A . The value of A determined from the
analysis is A = 1.3 & 0.7, which is in accord with a n earlier measurement [8].
I n Fig. 4, the solid line represents the calculated total yield of gamma rays
from the Cr53(p,.ny) Mn53 reaction. The experimental and theoretical curves
have been normalized arbitrarily. Good agreement between theory and experiment is found.
Conclusion
The present investigation of the (3%
( p ,n y ) Mn53 reaction shows that the
over-all agreement between the predictions of the CN theory and the measured
angular distributions, as well as the total gamma-ray yield, is quite good even
below 2.5 MeV. Further study of the ( p , n y ) reactions is desirable t o establish
the CN model adequacy for such processes.
The authors are indebted t o Professor M. EL-NADI foi encouragement
during this investigation. Grateful thanks are extended t o Dr.A. A. KRESNIK
for discussions. The author’s thanks are also due t o the accelerator staff for
efficient work as well t o A. OUZOYKENE
for his help in preparing the article for
publication. Two of us (A. I. P . and V. E. S.) would like t o thank the authorities of the UAR Atomic Energy Establishment for their hospitality.
References
[l] SHELDON,
E., Rev. Mod. Physics 35 (1963) 795.
[2] ABIJZEID, M. A., M. I. EL-ZAIKI, N. A. MANSOUR,A. I. POPOV,H. R. SAADand
V. E. STORIZHKO
(to be published).
J. A., J. J. G . MCCUEand W. M. PRESTON,
Physic. Rev. 85 (1952) 585.
[3] LOVINQTON,
C. L., C. GOOD-MANand P. H. STELSON,
Physic. Rev. 86 (1952)
[4] MCCLELLANDE,
631 A.
[5] VALTER,A. K., I. 1.ZALOUBOVSKY,
A. P. KLUCIIAREV
and V. A. LOUTSIK,Nuclear
reactions at low and medium energies (Academy of Science USSR, Moscow, 1958,279).
[6] KIM, H. I., Oak Ridge National Laboratory Report No ORNL 0-674 (1954), Phys.
Letters 14 (1965) 51.
171 JOHNSON, C. H., C. C. TRAIL,and A. GALONSKY,
Physic. Rev. 136 (1964) B 1719.
25, D.C., sheet
[8] Nuclear Data Sheets, National Academy of Sciences, Washington
61-3-47.
HANSER,
W., and H. FESHBACH,
Physic. R.ev. 87 (1952) 368.
SATCHLER,
G. R., Physic. Rev. 94 (1954) 1304; 104 (1956) 1198.
FERENZ,
M., and N. ROSENZWEIG,
Argonne Report ANL-5324 (1955).
SATCHLER,
G. R., Proc. physic. SOC.(London) A 66 (1965) 1081.
Can. J. Phys. 48 (1966) 1446.
GILBERT,A., and A. G. W. CAMERON,
P. E., Modern Nuclear Models (Atomizdat, Moskow, 1960).
NEMIROVSKY,
FESHBACH,
H., M.M. SHAPIRO,
and V. F. WEISSKOPF,
NYO-3377, NDA Report 15B-5
(June 15, 1953).
Ca.iro (Egypt), Atomic Energy Establishment.
Bei der Redaktion eingegangen am 29. Dezember 196G.
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